4180 papers
This paper establishes sharp quantitative integral inequalities for a general family of conformally invariant extension operators and their adjoints by developing a refined analysis of hypergeometric functions, thereby extending previous results to the full admissible parameter range.
This paper establishes the equivalence between Bogomolov's instability theorem and the Miyaoka-Sakai theorem on surfaces in positive characteristic, demonstrating how their interplay yields partial vanishing results, new proofs for Kawamata-Viehweg vanishing on del Pezzo surfaces, and Reider-type results for Fujita's conjecture.
This paper constructs new cotorsion pairs in an abelian category by gluing cotorsion pairs from a recollement's outer components, establishes conditions for their coincidence and completeness, and applies these results to Morita rings while introducing a specific class of recollements with enhanced homological properties.
This paper establishes that quadratic congruences modulo hold for a wide range of half-integral weight cusp forms with the eta multiplier and an arbitrary Dirichlet character, extending previous results limited to real characters through the study of modular Galois representations and a new theorem on the existence of specific conjugacy classes in their images.
This paper introduces the class of -cuttable undirected phylogenetic networks as a computationally useful alternative to tree-child-orientable networks, demonstrating that they are recognizable in polynomial time and render the NP-hard Tree Containment problem solvable in polynomial time for .
This paper establishes the local and global well-posedness, quenching criteria, and asymptotic convergence rates (exponential or algebraic) of solutions to a second-order nonlocal parabolic MEMS equation by employing operator semigroups, Lojasiewicz–Simon inequalities, and numerical validation.
This paper introduces a novel Fréchet regression framework for multivariate distributional responses that leverages the nonparanormal transport metric to efficiently decompose the problem into marginal and dependence regressions, offering theoretical guarantees on convergence and dimensionality while demonstrating practical utility in continuous glucose monitoring.
This paper introduces a novel construction of local Morse homology to compute the homology of critical points in the Lagrange problem, thereby proving that linear critical points are either saddle points or degenerate, refining the previous conclusion that they must be saddle points if non-degenerate.
This paper provides a comprehensive survey of various Waring-type problems across the mathematical structures of groups, Lie algebras, and associative algebras.
This paper introduces the bicomplex Prabhakar derivative by extending fractional calculus to four-dimensional bicomplex spaces, establishing its fundamental operational properties and integral representations to provide a versatile framework for modeling complex phenomena with memory effects and multi-dimensional coupling.
This paper investigates the asymptotic behaviors of global solutions to fourth-order parabolic and hyperbolic equations modeling Micro-Electro-Mechanical Systems (MEMS) under Dirichlet boundary conditions, establishing their convergence to equilibrium with rate estimates and supporting numerical simulations.
This paper develops a wave function renormalization scheme within the Hamiltonian formalism to construct the ground state representation of interacting Hamiltonians for non-relativistic particles coupled to quantized relativistic fields, thereby addressing ultraviolet and infrared singularities in models like the spin-boson and Nelson systems.
This paper proposes a unified calibration framework that integrates heterogeneous internal and auxiliary information into randomized experiments under covariate-adaptive randomization via convex optimization, ensuring asymptotic validity and a no-harm efficiency guarantee while accommodating scenarios with growing numbers of strata and information sources.
This short note refutes two natural conjectures regarding polynomial count varieties by demonstrating that a smooth variety with a point count of is not necessarily isomorphic to affine space, and that such varieties do not necessarily have vanishing Hodge numbers for .
This paper establishes an optimal result for the differentiable normal linearization of partially hyperbolic diffeomorphisms by constructing a local conjugacy that is on the center manifold to achieve Takens' normal form without requiring non-resonant conditions, overcoming decoupling difficulties through a novel semi-decoupling method and advanced extension techniques.
This paper introduces a novel high-resolution ODE framework based on -resolution analysis to overcome the limitations of existing methods in studying first-order algorithms with momentum, providing deeper insights into their convergence properties and enabling provably optimal modifications for methods like PDHG and Heavy-Ball.
This paper demonstrates that single scalar field theories minimally coupled to a Carrollian connection and invariant under extended Carrollian transformations, including supertranslations, cannot support propagating modes because these symmetries force the energy density to be static and the momentum density to vanish.
This paper addresses an Erdős-Herzog-Piranian problem by proving that the maximum product of distances for diameter-2 point sets can be found among convex polygons, providing improved constructions over regular -gons and demonstrating that a general characterization of extremal polygons is impossible for even orders.
This paper develops a comprehensive Malliavin calculus for the Dirichlet–Ferguson process on a general phase space by deriving explicit chaos expansions, establishing fundamental operators and rules, and applying the framework to characterize the Fleming–Viot process and prove a Poincaré inequality.
This paper generalizes the Peter-Weyl Theorem by demonstrating that functions on locally compact groups with large nontrivial compact open subgroups can be approximated by locally representative functions.